On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo.

Area of Science:

• Computational Biology
• Statistical Genetics
• Bioinformatics

Background:

• Approximate Bayesian computation (ABC) is widely used for complex models in population genetics, epidemiology, and systems biology.
• Sequential Monte Carlo (SMC) methods are standard tools within ABC frameworks.
• Constructing effective perturbation kernels is crucial for guiding ABC SMC algorithms from prior to posterior distributions.

Purpose of the Study:

• To investigate the construction of perturbation kernels for ABC SMC.
• To derive optimality criteria for kernel selection based on Kullback-Leibler divergence.
• To demonstrate the performance benefits of optimized kernels in complex inference problems.

Main Methods:

• Derivation of optimality criteria for perturbation kernels using Kullback-Leibler divergence.
• Implementation and evaluation of locally adapted kernels within ABC SMC.
• Application to toy examples and demanding parameter inference problems in molecular biology.

Main Results:

• Locally adapted kernels demonstrate superior performance for complex posterior distributions.
• Optimized kernels lead to higher acceptance rates, offsetting their computational cost.
• Significant computational efficiency gains were observed in molecular biology applications.

Conclusions:

• The rational choice of perturbation kernels is critical for efficient ABC SMC.
• Locally adapted kernels are highly effective for challenging posterior inference.
• Optimized kernel selection substantially enhances the applicability of ABC SMC to complex biological data.